Is a good evaluation function as good as any of the extensions of alpha-beta pruning?
To build on Neil's answer a bit, you're right that the better your evaluation function gets, the less work your optimization function will need to perform. If your evaluation function gets good enough, you won't need to search at all.

This is not just an academic idea though! It's actually fairly widely used, and has been key to solving several games.

The first example I'm aware of is Tesauro's TD-Gammon player, from 1995. Tesauro used the ideas of reinforcement learning and self-play to train a Neural Network to act as an evaluation function. TD-Gammon played with just a 2-move lookahead using the best evaluation function that was found, and was deemed better than most (all?) human expert players at the time. 

More recently, AlphaGo Zero used similar techniques to solve Go, but learning both an evaluation function and (separately) a function to randomize over possible moves.